
\(\Lambda _c\ne 0\)  and \(T=0\) : In this case, we reproduce the results obtained for MAdS background which is dual to non-conformal field theory at zero temperature. The leading term corresponds to the conformal EoP and the non-conformal corrections appear as the sub-leading terms. These corrections are always positive and hence non-conformality increase \(\hat{E}_p(l\Lambda _c,l^{\prime }\Lambda _c)\) .

\(\Lambda _c=0\)  and \(T\ne 0\) : In this case, we reproduce the previous results obtained for AdS black hole, see for example [1]}. The leading term corresponds to the zero temperature EoP and the finite temperature correction appears as the sub-leading term. The constant \(C_3\)  is negative and hence the finite temperature corrections decrease \(\tilde{E}_p(lT,l^{\prime }T)\)  of our configuration.

\(\Lambda _c= 0\)  and \(T=0\) : We reach the previous results obtained for pure AdS\(_5\)  which is corresponding to the EoP of our configuration in zero temperature conformal field theory [2]}. Obviously, this term is positive.

